Sum of series x²-16

Given number:
$$x^{2} - 16$$
It is a series of species
$$a_{x} \left(c x - x_{0}\right)^{d x}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}$$
In this case
$$a_{x} = x^{2} - 16$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty} \left|{\frac{x^{2} - 16}{\left(x + 1\right)^{2} - 16}}\right|$$
Let's take the limit
we find

True

False